Mazur's inequality and laffaille's theorem

Christophe Cornut

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arXiv · 1509.00574

Mazur's inequality and laffaille's theorem

Christophe Cornut

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Abstract

We look at various questions related to filtrations in $p$-adic Hodgetheory, using a blend of building and Tannakian tools. Specifically,Fontaine and Rapoport used a theorem of Laffaille on filtered isocrystalsto establish a converse of Mazur's inequality for isocrystals. Wegeneralize both results to the setting of (filtered) $G$-isocrystalsand also establish an analog of Totaro's $\otimes$-product theoremfor the Harder-Narasimhan filtration of Fargues.

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Christophe Cornut. 2019-10-29. Mazur's inequality and laffaille's theorem. https://arxiv.org/abs/1509.00574

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